Developer(s) | Tomlab Optimization Inc. |
---|---|
Stable release | 8.7 / 17 September 2020 |
Written in | MATLAB, C, Fortran |
Operating system | Windows 32/64-bit, Linux 32/64-bit and Mac OS X (Intel) |
Size | 89 MB (Windows 32-bit) |
Type | Technical computing |
License | Proprietary |
Website | TOMLAB product page |
The TOMLAB [1] [2] [3] Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
TOMLAB is a general purpose development and modeling environment [4] in MATLAB for research, teaching and practical solution of optimization problems. It enables a wider range of problems to be solved in MATLAB and provides many additional solvers.
TOMLAB supports solvers like CPLEX, SNOPT, KNITRO and MIDACO. Each such solver can be called to solve one single model formulation. The supported solvers are appropriate for many problems, including linear programming, integer programming, and global optimization.
An interface to AMPL makes it possible to formulate the problem in an algebraic format. The MATLAB Compiler enables the user to build stand-alone solutions. Sister products are available for LabVIEW and Microsoft .NET.
Modeling is mainly facilitated by the TomSym class.
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.
AMPL is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing . It was developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories. AMPL supports dozens of solvers, both open source and commercial software, including CBC, CPLEX, FortMP, MINOS, IPOPT, SNOPT, KNITRO, and LGO. Problems are passed to solvers as nl files. AMPL is used by more than 100 corporate clients, and by government agencies and academic institutions.
IBM ILOG CPLEX Optimization Studio is an optimization software package.
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Python and MATLAB are available.
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable.
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation. One particular advantage of some algebraic modeling languages like AIMMS, AMPL, GAMS, Gekko, MathProg, Mosel, and OPL is the similarity of their syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization, which is supported by certain language elements like sets, indices, algebraic expressions, powerful sparse index and data handling variables, constraints with arbitrary names. The algebraic formulation of a model does not contain any hints how to process it.
The PROPT MATLAB Optimal Control Software is a new generation platform for solving applied optimal control and parameters estimation problems.
nl is a file format for presenting and archiving mathematical programming problems. Initially, this format has been invented for connecting solvers to AMPL. It has also been adopted by other systems such as COIN-OR, FortSP, and Coopr.
The Zuse Institute Berlin is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany.
BARON is a computational system for solving non-convex optimization problems to global optimality. Purely continuous, purely integer, and mixed-integer nonlinear problems can be solved by the solver. Linear programming (LP), nonlinear programming (NLP), mixed integer programming (MIP), and mixed integer nonlinear programming (MINLP) are supported. In a comparison of different solvers, BARON solved the most benchmark problems and required the least amount of time per problem.
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies widely and is commonly used for solving problems in areas such as engineering, finance and computer science.
APOPT is a software package for solving large-scale optimization problems of any of these forms:
Optimization Toolbox is an optimization software package developed by MathWorks. It is an add-on product to MATLAB, and provides a library of solvers that can be used from the MATLAB environment. The toolbox was first released for MATLAB in 1990.
The FICO Xpress optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts. Xpress includes a general purpose non-linear solver, Xpress NonLinear, including a successive linear programming algorithm, and Artelys Knitro.
MINOS is a Fortran software package for solving linear and nonlinear mathematical optimization problems. MINOS may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities.
Convex Over and Under ENvelopes for Nonlinear Estimation (Couenne) is an open-source library for solving global optimization problems, also termed mixed integer nonlinear optimization problems. A global optimization problem requires to minimize a function, called objective function, subject to a set of constraints. Both the objective function and the constraints might be nonlinear and nonconvex. For solving these problems, Couenne uses a reformulation procedure and provides a linear programming approximation of any nonconvex optimization problem.
Deterministic global optimization is a branch of numerical optimization which focuses on finding the global solutions of an optimization problem whilst providing theoretical guarantees that the reported solution is indeed the global one, within some predefined tolerance. The term "deterministic global optimization" typically refers to complete or rigorous optimization methods. Rigorous methods converge to the global optimum in finite time. Deterministic global optimization methods are typically used when locating the global solution is a necessity, when it is extremely difficult to find a feasible solution, or simply when the user desires to locate the best possible solution to a problem.
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
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